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\begin{center}
\textbf{Vector Fields}

\textit{\textbf{Scalar and Vector Fields}}
\end{center}

\textbf{Question}

Determine the field lines of the following polar vector field.

$\un{F} = r\un{\hat{r}} - \un{\hat{\theta}}$


\textbf{Answer}

$\un{F} = r\un{\hat{r}} - \un{\hat{\theta}}$

The field lines satisfy $\frac{dr}{r} = -rd\theta$, or
$-\frac{dr}{r^2} = d\theta$.

So the field lines are the spirals $\frac{1}{r} = \theta + C$, or
$r=\frac{1}{(\theta + C)}$.


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